The references known to applicants considered to be the most pertinent to the present invention are:
(A) Sidles, "Noninductive Detection of Single-proton Magnetic Resonance", Applied Physics Letters, Vol. 58, Jun. 17, 1991, pp. 2854-2856;
(B) Garstens et al., "Low-field Magnetic Resonance", Physical Review, Vol. 99, 1955, pp. 459-462; and
(C) Abragam, "The Principles of Nuclear Magnetism", Oxford University Press, London, 1961, pp. 32-37, 65-71, and 86-87.
(D) Sidles, "Folded Stern-Gerlach Experiment As a Means for Detecting Nuclear Magnetic Resonance in Individual Nuclei", Physical Review Letters, Vol. 68, pp. 1124-1127.
References (A) and (D) described a method and apparatus for noninductively detecting the presence of nuclear magnetic resonance by coupling the nuclear spin of a particle to the motion of a mechanical oscillator, such as a quartz oscillator having two cantilevers shaped like a tuning fork. Coupling is achieved by applying a large-gradient magnetic field that exerts a mechanical force on the particle by virtue of its magnetic moment. The effectiveness of the coupling increases as the oscillator mass is decreased and the gradient length scale is made shorter. These references note that oscillator-based detection is only marginally effective for macroscopic samples, but is quite effective for single protons interacting with a micron-scale oscillator. They also suggest that magnetic resonance imaging may be possible on a molecular scale.
The mechanical cantilevers described in Reference (A) for use in molecular imaging have resonance frequencies that are designed to coincide with the resonant frequency of the precessing nuclear spins, which is typically in the range of 10-600 MHz. It is difficult to build a suitable mechanical cantilever with such high frequencies because, for molecular imaging, it is desirable that the cantilevers have a low spring constant in order to provide adequate force sensitivity. High resonant frequency and a low spring constant can be achieved only if the cantilevers have very low mass, which implies small physical size. Reference (A) proposes molecular imaging by the use of cantilevers with dimensions as small as 5 nanometers, which is too small for present-day micromechanical fabrication techniques.
The basic problem with direct mechanical detection of nuclear precessing spins in a spin resonance implementation, such as in Reference (A), is that the spin resonance frequency is inconveniently high. In nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR), the spin resonance frequency .omega..sub.0 is given by .omega..sub.0 =.gamma.H.sub.z, where .gamma. is the gyromagnetic ratio and H.sub.z is the applied field used to polarize the sample (i.e., to create a difference in the energy and population of the parallel and anti-parallel spin states). For best sensitivity, H.sub.z is usually made as large as practical. Making H.sub.z large creates a desirably large net magnetic moment in the sample, but also makes the spin resonance frequency .omega..sub.0 larger than is practical to detect mechanically. In ferromagnetic resonance (FMR), H.sub.z is an effective field that includes the effect of quantum mechanical exchange energy. In nuclear quadrupole resonance (NQR), spin state energy splitting is created by the interaction of the nuclear electric quadrupole moment with the gradient of the local electric fields in the molecule or crystal.
Reference (B) discusses the steady state behavior of magnetic resonance as a function of applied field and frequency; and, in particular, equation (11) on page 461 describes the behavior of M.sub.z, the magnetization in the z direction.
Reference (C) is a text describing the general principles of NMR and the specific pages cited disclose various techniques for modulating the magnetization, including magnetization in the z direction (M.sub.z). These techniques include adiabatic fast passage, transient nutation, and the application of high-frequency pulses.
There is a need for an alternative magnetic force detection method and apparatus which (1) does not require a cantilever or cantilevers to have a resonant frequency equal to the frequency of the precessing spins, thereby permitting use of cantilevers with low-resonant frequency (e.g., 1-10,000 kHz) that are commercially available; (2) is suitable for all types of magnetic resonance, including NMR, EPR, FMR, NQR, antiferromagnetic resonance, and ferrimagnetic resonance; and (3) is useful for magnetic resonance force microscopy (e.g., for high-resolution imaging of molecules or imaging below surfaces with good resolution and the ability to evaluate the type of material by nuclear magnetic resonance spectroscopy, such as for nondestructive imaging of biological cells or of fully encapsulated integrated circuits.)